(i) Field of the Invention
The present invention relates in general to measuring devices, and particularly to a measuring device designed to be used in drawing a line perpendicular to a reference line. More particularly, the invention relates to measuring devices that utilize multiple scales that are related by the Pythagorean theorem to facilitate the drawing of a line perpendicular to a reference line from a point on the reference line.
(ii) Description of the Related Art
In the construction of buildings, houses, and the like, it is often necessary to make a line that is perpendicular to an existing wall, structure or reference line. For example, this need typically arises when the building specifications specify a wall to bebuilt perpendicular to another wall. In this situation, the reference line may be a marking on the floor or a wall that has already been framed and the desired perpendicular line is going to be used to mark the location to build the perpendicular wall.
To construct the perpendicular line, builders have employed numerous techniques over the years. The simplest technique involves the use of a square. The builder places a first edge of the square along the reference line and then draws a perpendicular line by making a mark along a second edge of the square. The use of a square, however, is limited by its physical dimensions and can not be utilized to accurately draw a line perpendicular to a reference line that is longer in length than the square. Attempts to extend the length of the drawn perpendicular line introduce error and the extended line usually deviates from perpendicular as the line is extended. The use of a square, therefore, is not a viable option in situations where the perpendicular line needs to be longer than 1-3 feet.
Other prior art techniques employ the use of the Pythagorean theorem. Typically, a builder will utilize the well know and easily remembered relationship of a 3-4-5 right triangle. That is, a triangle with a first side 3 units in length (a unit being a dimensional measure of any linear scale, i.e. feet, meters, etc.), a second side 4 units in length and a hypotenuse 5 units in length will always be a right triangle with the first and second sides perpendicular to each other. Therefore, if either the first or second side runs along the reference line, the second or first side, respectively, will extend perpendicular to the reference line and can be used to mark a perpendicular line. Typically, a builder will mark a reference point on the reference line from which a perpendicular line is to be drawn. The builder will then scribe a first arc 3 units in radius from the reference point through an area generally believed to be perpendicular to the reference line from the reference point. The builder would then mark a second reference point on the reference line that is 4 units in length from the first reference point. Next, the builder would scribe a second arc 5 units in radius from the second reference point through the first arc. The first and second arcs intersecting at a third reference point. Finally, the builder would draw a line from the third reference point to the first reference point. The line connecting the first and third reference points would then be perpendicular to the reference line from the first reference point. The builder, if desired, can also use multiples of the 3-4-5 triangle if desired. For example, the builder can use a 6-8-10 triangle (a multiple of 2) in the same manner as the 3-4-5 triangle to draw a perpendicular line. The 3-4-5 triangle is popular because it is easy to remember and does not involve any calculations.
While this method has been used for a long time, there are inherent drawbacks to the use of the 3-4-5 triangle. In order to ensure the best accuracy in drawing the perpendicular line, it is desirable to make the two arcs intersect at a distance away from the reference wall that is longer than the perpendicular line needs to be drawn. However, the 3-4-5 triangle method is limited to lengths of 3 or 4 units away from the reference line or multiples thereof. In theory, any multiple of the 3-4-5 triangle could be employed to achieve the best accuracy, however, there are practical limitations to using multiples of the 3-4-5 triangle. If the demands of the specifications require a perpendicular line to be drawn that exceeds the 3 or 4 units in length then the builder will need to use multiples of the 3-4-5 triangle. Certainly, a competent builder can calculate a 2xc3x97multiple of the 3-4-5 triangle and perhaps even higher whole multiples. However, the whole multiples get large quickly and the lengths of the sides of the triangle may exceed the physical space limitations within which the builder can work. Therefore, it is very likely that a fractional multiple of the 3-4-5 triangle will need to be employed, to balance the physical space limitations against the desire to ensure the best accuracy. When a fractional multiple of the 3-4-5 triangle needs to be employed, the simplicity and ease of use is no longer present and a builder must resort to detailed calculations making the use of the 3-4-5 triangle not viable.
Another method of constructing perpendicular lines currently used by builders is the use of a preprogrammed calculator. Preprogrammed calculators are available that incorporate the use of the Pythagorean theorem to determine the lengths to utilize when constructing a right triangle to draw a perpendicular line. These preprogrammed calculators attempt to make the inputting of the available dimensions and the application of the results simple for the builder. However, there are many places in which an error can be introduced. For example, the builder must measure and then enter the available dimensions into the preprogrammed calculator. This introduces a potential for the incorrect measurement of the available space or the possibility of entering the information into the preprogrammed calculator incorrectly. The builder must also take the output of the preprogrammed calculator and use it to construct the right triangle, again introducing the potential for error. Additionally, the cost of the preprogrammed calculator is high and their durability is limited.
Finally, the builder can resort to using the Pythagorean theorem and a calculator to determine the dimensions of a right triangle to use to construct a line perpendicular to the reference line. However, this method introduces even more chances for error, is more complicated, and more time consuming than the use of the preprogrammed calculator because the builder must understand the Pythagorean theorem and how to utilize it to construct the desired right triangle. Therefore, the use of a calculator and the Pythagorean theorem is not a practical way of drawing a line perpendicular to a reference line.
Therefore, what is need is a simple apparatus and method to draw a line perpendicular to a reference line that is durable and easy to use. The apparatus and method should require little or no calculation by the builder and be inexpensive. Additionally, the apparatus and method should provide the most accurate perpendicular line possible while utilizing the maximum amount of space available for the builder to work in.
The present invention overcomes shortcomings of prior art devices by providing a measure that utilizes two scales and the Pythagorean theorem to allow a builder to quickly and easily draw a line perpendicular to a reference line. Furthermore, the present invention allows the builder to accurately draw a line perpendicular to a reference line with little or no calculations.
The present invention comprises both a method of determining perpendicular lines and an apparatus for determining perpendicular lines. The apparatus is comprised of a measure with a top surface having opposite first and second ends and opposite first and second edges. The first and second edges extend between the first and second ends. The top surface has a first set of indicia adjacent the first edge that represents a first scale. The top surface also has a second set of indicia adjacent the second edge that represents a second scale. The first and second sets of indicia have a common zero point. The second scale is a multiple of 1.4142 of the first scale.
In the preferred embodiment, the first scale is a true distance scale with the indicia setting forth the feet, inches, and fractions thereof in the well known conventional manner using lines of varying length and numbers to indicate the distance from the zero point. Alternatively, the first scale can have indicia that sets forth the true distance in meters, centimeters, and fractions thereof in the same manner. Preferably, the zero point is located at the first end. The measure can be a ruler, a folding ruler, a tape measure, or any other similar device. However, the measure is preferably a tape measure.
In another embodiment, the measure can have a bottom surface opposite the top surface. The bottom surface having a third set of indicia adjacent an edge which represents a third scale having a zero point. The bottom surface can also have a fourth set of indicia which represents a fourth scale having a zero point and is adjacent an edge opposite the third set of indicia. The fourth scale sharing the same zero point as the third scale.
The method of drawing a line perpendicular to a reference line using the preferred embodiment comprises marking a first reference point on the reference line from which it is desired to draw a line perpendicular to the reference line. Then selecting a reference distance to utilize in making the line perpendicular to the reference line and scribing a first arc the reference distance in radius as indicated on the first scale from the first reference point through an area generally believed to include a line perpendicular to the reference line from the first reference point. Next, a second reference point is marked on the reference line the reference distance in length as indicated on the first scale from the first reference point. Then a second arc is scribed the reference distance in radius as indicated on the second scale from the second reference point through the first arc with the first and second arcs intersecting at a third reference point. Finally, a line perpendicular to the reference line is drawn by drawing a line from the first reference point to the third reference point.
The builder utilizing this method and apparatus is not required to do any calculations. Additionally, the builder can choose any reference length to employ in using the method and can thereby take advantage of the maximum space available for drawing the line perpendicular to the reference line without sacrificing the accuracy of the line to be drawn. The measure of the invention provides a durable and inexpensive tool to utilize in drawing a line perpendicular to a reference line.
In an alternate embodiment, the apparatus comprises a measure with a top surface having opposite first and second ends and opposite first and second edges. The first and second edges extend between the first and second ends. The top surface has a first set of indicia adjacent the first edge that represents a first scale. The top surface also has a second set of indicia adjacent the second edge that represents a second scale. The first and second sets of indicia have a common zero point. The""second scale is a multiple of 1.732 of the first scale.
The method of drawing a line perpendicular to a reference line using the alternate embodiment comprises marking a first reference point on the reference line from which it is desired to draw a line perpendicular to the reference line. Then selecting a reference distance to utilize in making the line perpendicular to the reference line and scribing a first arc the reference distance in radius as indicated on the second scale from the first reference point through an area generally believed to include a line perpendicular to the reference line from the first reference point. Next a second reference point is marked on the reference line the reference distance in length as indicated on the first scale from the first reference point. Then a second arc is scribed two times the reference distance in radius as indicated on the first scale from the second reference point through the first arc with the first and second arcs intersecting at a third reference point. Finally, a line perpendicular to the reference line is drawn by drawing a line from the first reference point to the third reference point.
The builder utilizing this second method and apparatus is not required to do any calculations except for the doubling of the chosen reference length. Additionally, the builder can choose any reference length to employ in using the method and can thereby take advantage of the maximum space available for drawing the line perpendicular to the reference line without sacrificing the accuracy of the line to be drawn. The measure of this alternate embodiment of the invention also provides a durable and inexpensive tool to utilize in drawing a line perpendicular to a reference line.